Five-dimensional -symmetric spaces.
Flow-symmetric Riemannian manifolds.
Foliations by minimal surfaces and contact structures on certain closed 3-manifolds.
Four-dimensional ball-homogeneous and -spaces.
Four-dimensional Einstein metrics from biconformal deformations
Biconformal deformations take place in the presence of a conformal foliation, deforming by different factors tangent to and orthogonal to the foliation. Four-manifolds endowed with a conformal foliation by surfaces present a natural context to put into effect this process. We develop the tools to calculate the transformation of the Ricci curvature under such deformations and apply our method to construct Einstein -manifolds. Examples of one particular family have ends which collapse asymptotically...
From infinitesimal harmonic transformations to Ricci solitons
The concept of the Ricci soliton was introduced by R. S. Hamilton. The Ricci soliton is defined by a vector field and it is a natural generalization of the Einstein metric. We have shown earlier that the vector field of the Ricci soliton is an infinitesimal harmonic transformation. In our paper, we survey Ricci solitons geometry as an application of the theory of infinitesimal harmonic transformations.
-holonomy metrics connected with a 3-Sasakian manifold.
-natural metrics of constant curvature on unit tangent sphere bundles
We completely classify Riemannian -natural metrics of constant sectional curvature on the unit tangent sphere bundle of a Riemannian manifold . Since the base manifold turns out to be necessarily two-dimensional, weaker curvature conditions are also investigated for a Riemannian -natural metric on the unit tangent sphere bundle of a Riemannian surface.
Generalized plane wave manifolds
Generalized -space-forms
Generalized Symmetric Submanifolds of Euclidean Spaces.
Geodesic spheres and isometric flows
Geometric superrigidity.
Harmonic 4-Spaces.
Harmonic maps on contact metric manifolds
Harnack inequalities for curvature flows depending on mean curvature.
Holonomy groups of complete flat manifolds
We present short direct proofs of two known properties of complete flat manifolds. They say that the diffeomorphism classes of m-dimensional complete flat manifolds form a finite set and that each element of is represented by a manifold with finite holonomy group.
Holonomy groups of five dimensional Bieberbach groups.
Homogeneous Einstein metrics on flag manifolds.
Homogeneous Einstein Metrics on Spheres and Proiective Spaces.